# library(knitr)
# purl("h2fec_lifetime_MANOVA.Rmd", output = "h2fec_lifetime_MANOVA.R", documentation = 2)

Setup

set.seed(224819)

library(MCMCglmm)
## Loading required package: Matrix
## Loading required package: coda
## Loading required package: ape
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 2.2.1     ✔ purrr   0.2.4
## ✔ tibble  1.4.2     ✔ dplyr   0.7.4
## ✔ tidyr   0.8.0     ✔ stringr 1.3.0
## ✔ readr   1.1.1     ✔ forcats 0.3.0
## ── Conflicts ────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ tidyr::expand() masks Matrix::expand()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
library(parallel)

h2fec <- read.table("../../Data/Processed/eggs_per_vial.txt",
                    sep = '\t',
                    dec = ".", header = TRUE,
                    stringsAsFactors = FALSE)

# Standardize egg_total
h2fec$egg_total <- as.numeric(scale(h2fec$egg_total))

h2fec$animal <- seq(1, nrow(h2fec))
h2fec$treat <- as.factor(h2fec$treat)

pedigree <- h2fec[, c("animal", "sireid", "damid")]
names(pedigree) <- c("animal", "sire", "dam")
pedigree$animal <- as.character(pedigree$animal)
pedigree$sire <- as.character(pedigree$sire)
pedigree$dam <- as.character(pedigree$dam)
sires <- data.frame(animal = unique(pedigree$sire),
                    sire = NA, dam = NA, stringsAsFactors = FALSE)
dams <- data.frame(animal = unique(pedigree$dam),
                   sire = NA, dam = NA, stringsAsFactors = FALSE)
pedigree <- bind_rows(sires, dams, pedigree) %>%
  as.data.frame()

genet_corr <- tibble(model = character(),
                     HS_STD = numeric(),
                     LY_STD = numeric(),
                     HS_LY = numeric(),
                     n_eff = numeric())

iter <- 6.5e4
burnin <- 5e2
thinning <- 500
chains <- 12

rerun <- FALSE

MANOVA analysis

# 19 hours run time on nivalis (6e5 would be reasonable!)
if (rerun) {
  HS <- h2fec %>% 
    filter(treat == "HS") %>% rename(Eggs_HS = egg_total) %>% 
    as.data.frame()
  LY <- h2fec %>% 
    filter(treat == "LY") %>% rename(Eggs_LY = egg_total) %>% 
    as.data.frame()
  STD <- h2fec %>%
    filter(treat == "STD") %>% rename(Eggs_STD = egg_total) %>% 
    as.data.frame()
  
  h2fec_mrg <- full_join(full_join(HS, LY), STD)
  
  prior1 <- list(R = list(V = diag(3) * 1.002, nu = 1.002),
                 G = list(G1 = list(V = diag(3) * 1.002, nu = 0.002)))
  
  priors <- list(prior1)
  prior_names <- c("Tri: V = diag(3) * 1.002, nu = 0.02")
  
  for (ii in 1:length(priors)) {
    prior <- priors[[ii]]
    fm <- mclapply(1:chains, function(i) {
      MCMCglmm(cbind(Eggs_STD, Eggs_HS, Eggs_LY) ~ trait - 1,
               random = ~ us(trait):animal,
               rcov = ~ idh(trait):units,
               data = h2fec_mrg,
               prior = prior,
               pedigree = pedigree,
               family = rep("gaussian", 3),
               nitt = iter,
               burnin = burnin,
               thin = thinning)
    }, mc.cores = chains)
    outfile <- paste0("../../Data/Processed/FEC_lifetime_model_prior", ii, ".Rda")
    save(fm, file = outfile)
    
    re <- lapply(fm, function(m) m$VCV)
    re <- do.call(mcmc.list, re)
    re <- as.mcmc(as.matrix(re))
    
    n_eff <- effectiveSize(re)
    
    # STD vs. HS
    HS_STD <- re[ , "traitEggs_HS:traitEggs_STD.animal"] /
      sqrt(re[ , "traitEggs_STD:traitEggs_STD.animal"] *
             re[ , "traitEggs_HS:traitEggs_HS.animal"])
    
    # STD vs. LY
    LY_STD <- re[ , "traitEggs_LY:traitEggs_STD.animal"] /
      sqrt(re[ , "traitEggs_STD:traitEggs_STD.animal"] *
             re[ , "traitEggs_LY:traitEggs_LY.animal"])
    
    # LY vs. HS
    HS_LY <- re[ , "traitEggs_HS:traitEggs_LY.animal"] /
      sqrt(re[ , "traitEggs_LY:traitEggs_LY.animal"] *
             re[ , "traitEggs_HS:traitEggs_HS.animal"])
    
    genet_corr <- bind_rows(genet_corr,
                            tibble(model = prior_names[[ii]],
                                   HS_STD = median(HS_STD),
                                   LY_STD = median(LY_STD),
                                   HS_LY = median(HS_LY),
                                   n_eff = mean(n_eff)))
  }
  
  write_csv(genet_corr, path = "../../Data/Processed/Genetic_Correlations_Fecundity.csv")
}

Analyze model

load("../../Data/Processed/FEC_lifetime_model_prior1.Rda")

fe <- lapply(fm, function(m) m$Sol)
fe <- do.call(mcmc.list, fe)
plot(fe, ask = FALSE)

plot(fe[, 1, drop = FALSE], ask = FALSE)

plot(fe[, 2, drop = FALSE], ask = FALSE)

plot(fe[, 3, drop = FALSE], ask = FALSE)

# Extract random effects, convert to mcmc.list
re <- lapply(fm, function(m) m$VCV)
re <- do.call(mcmc.list, re)

plot(re[, 1, drop = FALSE], ask = FALSE)

plot(re[, 2, drop = FALSE], ask = FALSE)

plot(re[, 3, drop = FALSE], ask = FALSE)

autocorr.diag(re)
##           traitEggs_STD:traitEggs_STD.animal
## Lag 0                           1.000000e+00
## Lag 500                         2.982847e-01
## Lag 2500                        7.146360e-02
## Lag 5000                        1.294765e-02
## Lag 25000                       4.536912e-05
##           traitEggs_HS:traitEggs_STD.animal
## Lag 0                           1.000000000
## Lag 500                         0.156248238
## Lag 2500                        0.031417216
## Lag 5000                        0.003498503
## Lag 25000                      -0.001804021
##           traitEggs_LY:traitEggs_STD.animal
## Lag 0                           1.000000000
## Lag 500                         0.307534866
## Lag 2500                        0.056155721
## Lag 5000                        0.002550690
## Lag 25000                      -0.000144118
##           traitEggs_STD:traitEggs_HS.animal
## Lag 0                           1.000000000
## Lag 500                         0.156248238
## Lag 2500                        0.031417216
## Lag 5000                        0.003498503
## Lag 25000                      -0.001804021
##           traitEggs_HS:traitEggs_HS.animal
## Lag 0                          1.000000000
## Lag 500                        0.205638664
## Lag 2500                       0.037715531
## Lag 5000                       0.003537716
## Lag 25000                      0.005726066
##           traitEggs_LY:traitEggs_HS.animal
## Lag 0                         1.0000000000
## Lag 500                       0.3117063058
## Lag 2500                      0.0613418463
## Lag 5000                      0.0071330810
## Lag 25000                    -0.0004049636
##           traitEggs_STD:traitEggs_LY.animal
## Lag 0                           1.000000000
## Lag 500                         0.307534866
## Lag 2500                        0.056155721
## Lag 5000                        0.002550690
## Lag 25000                      -0.000144118
##           traitEggs_HS:traitEggs_LY.animal
## Lag 0                         1.0000000000
## Lag 500                       0.3117063058
## Lag 2500                      0.0613418463
## Lag 5000                      0.0071330810
## Lag 25000                    -0.0004049636
##           traitEggs_LY:traitEggs_LY.animal traitEggs_STD.units
## Lag 0                          1.000000000         1.000000000
## Lag 500                        0.334177198         0.217435079
## Lag 2500                       0.059986903         0.056694849
## Lag 5000                       0.007761136         0.012445564
## Lag 25000                     -0.001122749         0.002497479
##           traitEggs_HS.units traitEggs_LY.units
## Lag 0            1.000000000        1.000000000
## Lag 500          0.145979478        0.130891250
## Lag 2500         0.023375665        0.027294434
## Lag 5000         0.004060013        0.002802348
## Lag 25000        0.003316091       -0.001173931
effectiveSize(re)
## traitEggs_STD:traitEggs_STD.animal  traitEggs_HS:traitEggs_STD.animal 
##                           53045.91                           83325.49 
##  traitEggs_LY:traitEggs_STD.animal  traitEggs_STD:traitEggs_HS.animal 
##                           58057.52                           83325.49 
##   traitEggs_HS:traitEggs_HS.animal   traitEggs_LY:traitEggs_HS.animal 
##                           74656.12                           56228.85 
##  traitEggs_STD:traitEggs_LY.animal   traitEggs_HS:traitEggs_LY.animal 
##                           58057.52                           56228.85 
##   traitEggs_LY:traitEggs_LY.animal                traitEggs_STD.units 
##                           55399.82                           63875.46 
##                 traitEggs_HS.units                 traitEggs_LY.units 
##                           87607.67                           92173.28
# Concatenate samples
re <- as.mcmc(as.matrix(re))

head(re)
## Markov Chain Monte Carlo (MCMC) output:
## Start = 1 
## End = 7 
## Thinning interval = 1 
##      traitEggs_STD:traitEggs_STD.animal traitEggs_HS:traitEggs_STD.animal
## [1,]                         0.64571543                        0.31674791
## [2,]                         0.52673376                        0.32475664
## [3,]                         0.07073419                        0.08753511
## [4,]                         0.24399476                        0.23015828
## [5,]                         0.18447854                        0.17845981
## [6,]                         0.21805288                        0.18144762
## [7,]                         0.45349939                        0.22196209
##      traitEggs_LY:traitEggs_STD.animal traitEggs_STD:traitEggs_HS.animal
## [1,]                        0.14988896                        0.31674791
## [2,]                        0.15820538                        0.32475664
## [3,]                        0.02628937                        0.08753511
## [4,]                        0.09288334                        0.23015828
## [5,]                        0.06390203                        0.17845981
## [6,]                        0.07673514                        0.18144762
## [7,]                        0.14494084                        0.22196209
##      traitEggs_HS:traitEggs_HS.animal traitEggs_LY:traitEggs_HS.animal
## [1,]                        0.1804244                      0.081949572
## [2,]                        0.2088573                      0.097592717
## [3,]                        0.1416532                      0.003692021
## [4,]                        0.2311145                      0.070332167
## [5,]                        0.1887566                      0.050512395
## [6,]                        0.1622301                      0.064764942
## [7,]                        0.1781583                      0.071690710
##      traitEggs_STD:traitEggs_LY.animal traitEggs_HS:traitEggs_LY.animal
## [1,]                        0.14988896                      0.081949572
## [2,]                        0.15820538                      0.097592717
## [3,]                        0.02628937                      0.003692021
## [4,]                        0.09288334                      0.070332167
## [5,]                        0.06390203                      0.050512395
## [6,]                        0.07673514                      0.064764942
## [7,]                        0.14494084                      0.071690710
##      traitEggs_LY:traitEggs_LY.animal traitEggs_STD.units
## [1,]                       0.03839285           0.3721073
## [2,]                       0.04949449           0.4747530
## [3,]                       0.05623924           0.7739254
## [4,]                       0.05856316           0.5207588
## [5,]                       0.03187482           0.5467596
## [6,]                       0.02833080           0.5043791
## [7,]                       0.04704936           0.4127373
##      traitEggs_HS.units traitEggs_LY.units
## [1,]          0.1473181          0.4149074
## [2,]          0.1179832          0.3239175
## [3,]          0.1396977          0.3652965
## [4,]          0.1662813          0.3451403
## [5,]          0.1620903          0.3945810
## [6,]          0.1720018          0.4165490
## [7,]          0.1937566          0.3909889
# STD vs. HS
plot(re[ , "traitEggs_HS:traitEggs_STD.animal"])

plot(re[ , "traitEggs_STD:traitEggs_STD.animal"])

HS_STD <- re[ , "traitEggs_HS:traitEggs_STD.animal"] /
  sqrt(re[ , "traitEggs_STD:traitEggs_STD.animal"] *
         re[ , "traitEggs_HS:traitEggs_HS.animal"])
plot(HS_STD)

median(HS_STD)
## [1] 0.9465684
HPDinterval(HS_STD)
##          lower     upper
## var1 0.5623259 0.9994407
## attr(,"Probability")
## [1] 0.95
# STD vs. LY
LY_STD <- re[ , "traitEggs_LY:traitEggs_STD.animal"] /
  sqrt(re[ , "traitEggs_STD:traitEggs_STD.animal"] *
         re[ , "traitEggs_LY:traitEggs_LY.animal"])
plot(LY_STD)

median(LY_STD)
## [1] 0.8679601
HPDinterval(LY_STD)
##             lower     upper
## var1 -0.003012668 0.9991626
## attr(,"Probability")
## [1] 0.95
# LY vs. HS
HS_LY <- re[ , "traitEggs_HS:traitEggs_LY.animal"] /
  sqrt(re[ , "traitEggs_LY:traitEggs_LY.animal"] *
         re[ , "traitEggs_HS:traitEggs_HS.animal"])
plot(HS_LY)

median(HS_LY)
## [1] 0.8467249
HPDinterval(HS_LY)
##             lower     upper
## var1 -0.009809805 0.9988504
## attr(,"Probability")
## [1] 0.95

Plot for poster

library(tidyverse)
library(cowplot)
## 
## Attaching package: 'cowplot'
## The following object is masked from 'package:ggplot2':
## 
##     ggsave
B <- data_frame(`HS vs. STD` = as.numeric(HS_STD),
                `LY vs. STD` = as.numeric(LY_STD),
                `HS vs. LY` = as.numeric(HS_LY))

colMeans(B)
## HS vs. STD LY vs. STD  HS vs. LY 
##  0.8843495  0.7307286  0.7147110
B %>% gather(Comparison, value) %>%
  ggplot(aes(value, color = Comparison)) +
  geom_line(stat = "density", size = 2) +
  labs(x = "Genetic Correlation", y = "Density") +
  theme(legend.position = c(0.15, 0.85),
        text = element_text(size = 24),
        legend.text = element_text(size = 18))

ggsave(last_plot(), file = "Genetic_Correlation_Plot.pdf",
       width = 8, height = 6)

Model following Ingleby et al. 2013

Setup data as above

V_nu_to_a_b <- function(V, nu) {
  require(tidyverse)
  require(invgamma)
  
  a <- nu / 2
  b <- (nu * V) / 2
  
  p <- tibble(
    x = seq(0, 10, length = 200),
    y = dinvgamma(x, a, b)) %>% 
    ggplot(aes(x, y)) +
    geom_line()
  print(p)
  
  return(list(alpha = a, beta = b))
}
V_nu_to_a_b(1, 0.002)
## Loading required package: invgamma
## Warning: Removed 1 rows containing missing values (geom_path).

## $alpha
## [1] 0.001
## 
## $beta
## [1] 0.001
if (rerun) {
  
  prior1 <- list(R = list(V = 1, nu = 0.002),
                 G = list(G1 = list(V = diag(3) / 3, nu = 0.002)))
  
  prior2 <- list(R = list(V = 1, nu = 0.002),
                 G = list(G1 = list(V = diag(3) * 0.5 * 0.7, nu = 0.002)))
  
  M <- matrix(0.5 * 0.7, 3, 3)
  diag(M) <- 0.5
  prior3 <- list(R = list(V = 1, nu = 0.002),
                 G = list(G1 = list(V = M, nu = 0.002)))
  
  priors <- list(prior1, prior2, prior3)
  prior_names <- c("Sire: V = diag(3) / 3, nu = 0.002",
                   "Sire: V = diag(3) * 0.5 * 0.7, nu = 0.002",
                   "Sire: V = 0.5 diag, 0.35 off-diag, nu = 0.002")
  
  h2fec$egg_total_std <- scale(h2fec$egg_total)
  
  for (ii in 1:length(priors)) {
    prior <- priors[[ii]]
    
    fm <- mclapply(1:chains, function(i) {
      MCMCglmm(egg_total_std ~ treat,
               random = ~ us(treat):sireid,
               data = h2fec,
               prior = prior,
               family = "gaussian",
               nitt = iter,
               burnin = burnin,
               thin = thinning,
               verbose = TRUE)
    }, mc.cores = chains)
    
    outfile <- paste0("sire_model_prior", ii, ".Rda")
    save(fm, file = outfile)
    
    re <- lapply(fm, function(m) m$VCV)
    re <- do.call(mcmc.list, re)
    re <- as.mcmc(as.matrix(re))
    n_eff <- effectiveSize(re)
    
    # STD vs. HS
    HS_STD <- re[ , "treatHS:treatSTD.sireid"] /
      sqrt(re[ , "treatHS:treatHS.sireid"] *
             re[ , "treatSTD:treatSTD.sireid"])
    median(HS_STD)
    
    # STD vs. LY
    LY_STD <- re[ , "treatSTD:treatLY.sireid"] /
      sqrt(re[ , "treatSTD:treatSTD.sireid"] *
             re[ , "treatLY:treatLY.sireid"])
    median(LY_STD)
    
    # LY vs. HS
    HS_LY <- re[ , "treatHS:treatLY.sireid"] /
      sqrt(re[ , "treatLY:treatLY.sireid"] *
             re[ , "treatHS:treatHS.sireid"])
    median(HS_LY)
    
    genet_corr <- bind_rows(genet_corr,
                            tibble(model = prior_names[[ii]],
                                   HS_STD = median(HS_STD),
                                   LY_STD = median(LY_STD),
                                   HS_LY = median(HS_LY),
                                   n_eff = mean(n_eff)))
    
  }
  write_csv(genet_corr, path = "Genetic_Correlations.csv")
  
  kable(genet_corr, digits = 3)
}

Analyze model

load("sire_model_prior1.Rda")

fe <- lapply(fm, function(m) m$Sol)
fe <- do.call(mcmc.list, fe)
plot(fe, ask = FALSE)

# Extract random effects, convert to mcmc.list
re <- lapply(fm, function(m) m$VCV)
re <- do.call(mcmc.list, re)

plot(re[, 1:3], ask = FALSE)

plot(re[, 4:6], ask = FALSE)

plot(re[, 7:9], ask = FALSE)

plot(re[, 10], ask = FALSE)

effectiveSize(re)
##   treatHS:treatHS.sireid   treatLY:treatHS.sireid  treatSTD:treatHS.sireid 
##                 154676.0                 153969.3                 154806.7 
##   treatHS:treatLY.sireid   treatLY:treatLY.sireid  treatSTD:treatLY.sireid 
##                 153969.3                 153457.9                 153747.7 
##  treatHS:treatSTD.sireid  treatLY:treatSTD.sireid treatSTD:treatSTD.sireid 
##                 154806.7                 153747.7                 156337.6 
##                    units 
##                 155935.2
# Concatenate samples
re <- as.mcmc(as.matrix(re))
colnames(re)
##  [1] "treatHS:treatHS.sireid"   "treatLY:treatHS.sireid"  
##  [3] "treatSTD:treatHS.sireid"  "treatHS:treatLY.sireid"  
##  [5] "treatLY:treatLY.sireid"   "treatSTD:treatLY.sireid" 
##  [7] "treatHS:treatSTD.sireid"  "treatLY:treatSTD.sireid" 
##  [9] "treatSTD:treatSTD.sireid" "units"
# ??? Heritability ????
HS <- re[, "treatHS:treatHS.sireid"] / (re[, "treatHS:treatHS.sireid"] + re[, "units"])
median(HS)
## [1] 0.06874132
LY <- re[, "treatLY:treatLY.sireid"] / (re[, "treatLY:treatLY.sireid"] + re[, "units"])
median(LY)
## [1] 0.0466465
STD <- re[, "treatSTD:treatSTD.sireid"] / (re[, "treatSTD:treatSTD.sireid"] + re[, "units"])
median(STD)
## [1] 0.2953422
# STD vs. HS
HS_STD <- re[ , "treatHS:treatSTD.sireid"] /
  sqrt(re[ , "treatHS:treatHS.sireid"] *
         re[ , "treatSTD:treatSTD.sireid"])
plot(HS_STD)

median(HS_STD)
## [1] 0.9166127
HPDinterval(HS_STD)
##           lower     upper
## var1 0.08404823 0.9996949
## attr(,"Probability")
## [1] 0.95
# STD vs. LY
LY_STD <- re[ , "treatSTD:treatLY.sireid"] /
  sqrt(re[ , "treatSTD:treatSTD.sireid"] *
         re[ , "treatLY:treatLY.sireid"])
plot(LY_STD)

median(LY_STD)
## [1] 0.8522464
HPDinterval(LY_STD)
##          lower     upper
## var1 -0.245345 0.9995995
## attr(,"Probability")
## [1] 0.95
# LY vs. HS
HS_LY <- re[ , "treatHS:treatLY.sireid"] /
  sqrt(re[ , "treatLY:treatLY.sireid"] *
         re[ , "treatHS:treatHS.sireid"])
plot(HS_LY)

median(HS_LY)
## [1] 0.7617521
HPDinterval(HS_LY)
##          lower     upper
## var1 -0.588665 0.9992035
## attr(,"Probability")
## [1] 0.95